This invention relates to optical processors, and more particularly to optical processors for performing real-time correlations.
Under many circumstances an acoustic or electromagnetic signal is received from a moving source and information as to the location and velocity of the source is desirable. Examples of where this occurs are undersea surveillance and radar surveillance. A common method of representing this is on a graph known as an ambiguity plane, where velocity is plotted against distance. The relative doppler shift and time shift between two signals so received can be used to extract this data.
The ambiguity plane is prepared by evaluating the ambiguity integral which is defined as EQU .chi.(.omega.,.tau.)=.intg.S.sub.1 (t)S.sub.2 *(t-.tau.)e.sup.-i.omega.t dt (1)
In this equation S.sub.1 (t) and S.sub.2 (t) are two signals being compared expressed as functions of time. The variable .tau. is introduced to correct for the fact that although it is expected that S.sub.1 (t) and S.sub.2 (t) should have a similar form, they will, in general, be shifted in time relative to each other. The function S.sub.2 *(t-.tau.) is the complex conjugate of S.sub.2 (t-.tau.) which is the time shifted version of the signal actually received. The factor e.sup.-i.omega.t is introduced to correct for the frequency difference between S.sub.1 (t) and S.sub.2 (t) caused by the Doppler effect. The values of .omega. and .tau. which yield a maximum value of the ambiguity integral may be used to extract information about the velocity and range of the object under surveillance.
FIG. 1 shows a typical situation where ambiguity processing is used. A target 10 emits a signal, represented by arrows 11, in all directions. The signal is received by a first receiver 12 and a second receiver 13. It is clear that if the target is moving there will be a different. Doppler shift observed by the two receivers 12 and 13. If the receivers 12 and 13 are different distances from the target 10 the signals 11 will also arrive at different times. Therefore the signal observed by receiver 12 is of the form EQU S.sub.1 (t)=f(t)e.sup.i.omega..sbsp.1.sup.t ( 2)
and the signal S .sub.2 (t) observed by receiver 13 is of the form EQU S.sub.2 (t)=f(t+t.sub.o)e.sup.i.omega..sbsp.2.sup.( t+t.sbsp.o.sup.) ( 3)
In these expressions f(t) may be regarded as a function modulating a carrier wave. In equation (3) t.sub.o is a constant which expresses the difference of propagation time for the signal received by the first receiver 12 and the second receiver 13. In general t.sub.o may be positive, negative or zero. If t.sub.o is positive, the signal arrives at receiver 12 before it arrives at receiver 13. If t.sub.o is negative the signal arrives at receiver 13 first. If t.sub.o is zero both receivers 23 and 13 receive the signal at the same time. The terms e.sup.i.omega..sbsp.1.sup.t and e.sup.i.omega..sbsp.2.sup.(t+t.sbsp.o.sup.) are carrier waves of angular frequency .omega..sub.1 and .omega..sub.2 respectively. The difference between .omega..sub.1 and .omega..sub.2 is the relative Doppler shift. It is clear that the ambiguity function of equation (1) will take on a maximum value when EQU .tau.=t.sub.o and .omega.=.omega..sub.1 -.omega..sub.2. (4)
It should be noted that these signals could arise from radar surveillance, as shown in FIG. 2. In the case of radar, a transmitter 14 emits a signal 15. Signal 15 is designated S.sub.1 (t) and has the form shown in equation (2). Signal 15 strikes target 16 and returns as reflected signal 17. Reflected signal 17 is received by receiver 18. Reflected signal 17 is designated S.sub.2 (t) and has the form of equation (3) where t.sub.o is the time elapsed between the transmission of signal 15 by transmitter 14 and the reception of reflected signal 17 by receiver 18. For radar surveillance, t.sub.o will always be positive. If the target 16 is moving relative to transmitter 14 and receiver 18, .omega..sub.2 will be Doppler shifted from the original value of .omega..sub.1. The following analysis applies equally to the situations shown in FIGS. 1 and 2.
Evaluation of the ambiguity integral .chi.(.omega.,.tau.) can, of course, be implemented on a digital computer. However, this is a difficult and time-consuming task because of the two-dimensional nature of .chi.(.omega.,.tau.). Similarly 1-D analog or digital matched filters (e.g., tapped delay lines) can compute .chi.(.omega.,.tau.) only with a two-step approach. For example, if S.sub.2 (t) is the radar return signal with a Doppler shift, all possible shifts are investigated, with Eq. (1) being computed for each possible value of .omega..
Since optics is inherently two-dimensional, people have naturally sought to implement .chi.(.omega.,.tau.) optically. Several methods have been successfully demonstrated, while others are conceptual only.
An examination of equation (1) reveals a strong similarity to a Fourier transform. If F.sub.t is the Fourier transform operator which acts on the time variable, the following definition applies: EQU F.sub.t [g(t,.tau.)]=.intg.g(t,.tau.)e.sup.i.omega.t dt (5)
If g(t,.tau.) is taken to be EQU g(t,.tau.)=S.sub.1 (t)S.sub.2 *(t+.tau.) (6)
it is apparent that a simple substitution will make equation (1) and equation (5) identical. Therefore in the prior art, the product of S.sub.1 (t) and S.sub.2 *(t+.tau.) of equation (6) is produced and optically Fourier transformed to evaluate equation (1).
The traditional approach has been to set up an image plane correlator and at the image or Fourier plane, insert a film or spatial light modulator containing rows of data consisting of shifted versions of S.sub.2 (t). Equation (1) is then implemented by Fourier transforming along one axis to produce the .omega. axis on the output and imaging along the other axis to produce the correlation on the .tau. axis of the output.
Use of film or even present-day spatial light modulators is undesirable because of the slow rate at which information can be written and changed. More recently, near-real-time generation of ambiguity surfaces has been accomplished using acousto-optic techniques. Acousto-optic techniques may be classified as being either time-integrating or space-integrating. The space-integrating techniques generally use the idea of Fourier transformation in one dimension and imaging in the other.
In a typical prior art space-integrating system, coherent light from a laser is expanded and collimated by lenses, and impinges on a data mask having the function S.sub.2 *(t+.tau.) encoded thereon in the form of lines. The t variable is represented in the horizontal direction and the .tau. variable in the vertical. A lens images the data mask on another data mask which is encoded with S.sub.1 (t) represented by lines. As a result the light passing the second data mask is encoded with the product S.sub.1 (t)S.sub.2 *(t+.tau.). The light next passes through a cylindrical lens and a spherical lens and arrives at the ambiguity plane. The resultant image is Fourier transformed in the horizontal or t dimension and imaged in the vertical or .tau. dimension. Therefore the image represents the integral (1). The maximum value appears as the point of greatest light intensity, i.e. the brightest point.
Such processors are called space-integrating optical processors because the integration operation required in equation (5) is obtained by a lens collecting and focusing light rays over a region of space defined by the second data mask.
The data masks are produced by the use of a two-dimensional spatial light modulator. Production of a mask with such a modulator requires many linear scans and is the limiting factor on the speed of the system. U.S. Pat. No. 4,071,907 issued to David Paul Casasent shows an improvement by substituting an electronically-addressed light modulator (EALM) tube for one of the data masks. An EALM tube is a multiple scan unit, however, with the same limitations inherent in all present-day two-dimensional light modulators, i.e., slow rate at which information can be written or changed (&lt;100 frames/sec).
A second limitation arises with space-integrating processors; the data S.sub.1 (t) and S.sub.2 *(t+.tau.) must fit in their entirety onto the two data masks, respectively. This limitation also applies to other prior-art space-integrating processors such as in U.S. Pat. No. 4,310,894 issued to T. C. Lee, et al., where acoustic cells are used in place of the data masks. The length of the acoustic cell determines the maximum length signals permissible.
Time-integration approaches generally utilize chirp (linear FM waveform) techniques whereby signal S.sub.1 or S.sub.2 must be premultiplied with a chirp and later correlated with a second chirp to obtain .chi.(.omega.,.tau.). Such processors are called time-integrating optical processors because time integration of an optical signal onto a photodetector array is used to effect the integral in equation (5). In a typical prior art time-integrating system such as disclosed in U.S. Pat. No. 4,225,938 issued to T. M. Turpin, a laser light source produces a light beam which is intensity-modulated by an acousto-optic modulator with signal h(t). The modulated light is then passed through two acousto-optic Bragg cells which are oriented orthogonal to each other and which are respectively driven by signals g.sub.x (t) and g.sub.y (t). The signals g.sub.x (t) and g.sub.y (t) produce additional diffractions of the light, and the finally diffracted light beam intensity is integrated at a two-dimensional detector array. The ambiguity function .chi.(.omega.,.tau.) can be obtained in two ways. One is to use a moving mirror to introduce Doppler shifts onto a second light beam which is interfered with the final diffracted beam from the second Bragg cell.
However, a more common approach disclosed by J. D. Cohen in Proc. SPIE, 180, 134 (1979) is to eliminate the mirrors and utilize a chirp-transform technique. The signal f.sub.x (t)=S.sub.1 (t) is multiplied by a chirp function f.sub.y (t)=exp (it.sup.2 /2), using a mixer, producing the resultant signal h(t) to the acousto-optic modulator. The inputs g.sub.x (t) and g.sub.y (t) are chosen to be g.sub.x (t)=S.sub.2 *(t) and g.sub.y (t)=exp(it.sup.2 /2). The resultant integrated signal on the photodetector array is EQU .chi.(.omega.,.tau.)=.intg..sub.t S.sub.1 (t)S.sub.2 *(t-.tau.)exp(i.omega.t)dt (7)
where .tau. is y/v, with v the acoustic wave velocity in the Bragg cell which is driven by the signal g.sub.y (t).
The time integrating systems do not have a limit on maximum signal length permissable. They do however, suffer from reliance on mechanically moving parts or from the complexity of a chirp-transform architecture.